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Volumn 19, Issue 2, 2002, Pages 227-248

Derivation and Implementation of Two-Step Runge-Kutta Pairs

Author keywords

Implementation aspects; Local error estimation; Order conditions; Two step Runge Kutta methods

Indexed keywords


EID: 0042840802     PISSN: 09167005     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF03167454     Document Type: Article
Times cited : (26)

References (26)
  • 1
    • 0023329035 scopus 로고
    • A new theoretical approach to Runge-Kutta methods
    • P. Albrecht, A new theoretical approach to Runge-Kutta methods. SIAM J. Numer. Anal., 24 (1987), 391-406.
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 391-406
    • Albrecht, P.1
  • 3
    • 0009619039 scopus 로고    scopus 로고
    • The Runge-Kutta theory in a nutshell
    • P. Albrecht, The Runge-Kutta theory in a nutshell. SIAM J. Numer. Anal., 33 (1996), 1712-1735.
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1712-1735
    • Albrecht, P.1
  • 4
    • 0032344798 scopus 로고    scopus 로고
    • Construction of two-step Runge-Kutta methods of high order for ordinary differential equations
    • Z. Bartoszewski and Z. Jackiewicz, Construction of two-step Runge-Kutta methods of high order for ordinary differential equations. Numerical Algorithms, 18 (1998), 51-70.
    • (1998) Numerical Algorithms , vol.18 , pp. 51-70
    • Bartoszewski, Z.1    Jackiewicz, Z.2
  • 5
    • 85034524641 scopus 로고    scopus 로고
    • Toward a two-step Runge-Kutta code for nonstiff differential systems
    • To appear
    • Z. Bartoszewski and Z. Jackiewicz, Toward a two-step Runge-Kutta code for nonstiff differential systems. To appear in Appl. Math.
    • Appl. Math.
    • Bartoszewski, Z.1    Jackiewicz, Z.2
  • 7
    • 0031212298 scopus 로고    scopus 로고
    • Order conditions for two-step Runge-Kutta methods
    • J.C. Butcher and S. Tracogna, Order conditions for two-step Runge-Kutta methods. Appl. Numer. Math., 24 (1997), 351-364.
    • (1997) Appl. Numer. Math. , vol.24 , pp. 351-364
    • Butcher, J.C.1    Tracogna, S.2
  • 8
    • 0005366895 scopus 로고
    • Pseudo-Runge-Kutta methods involving two points
    • G.D. Byrne and R.J. Lambert, Pseudo-Runge-Kutta methods involving two points. J. Assoc. Comput. Mach., 13 (1966), 114-123.
    • (1966) J. Assoc. Comput. Mach. , vol.13 , pp. 114-123
    • Byrne, G.D.1    Lambert, R.J.2
  • 9
    • 0005300783 scopus 로고
    • A class of pseudo Runge-Kutta methods
    • R. Caira, C. Costabile and F. Costabile, A class of pseudo Runge-Kutta methods. BIT, 30 (1990), 642-649.
    • (1990) BIT , vol.30 , pp. 642-649
    • Caira, R.1    Costabile, C.2    Costabile, F.3
  • 10
    • 0009345728 scopus 로고    scopus 로고
    • Collocation-based two-step Runge-Kutta methods
    • N. huu Cong and T. Mitsui, Collocation-based two-step Runge-Kutta methods. Japan J. Indust. Appl. Math., 13 (1996), 171-183.
    • (1996) Japan J. Indust. Appl. Math. , vol.13 , pp. 171-183
    • Huu Cong, N.1    Mitsui, T.2
  • 12
    • 0005297545 scopus 로고    scopus 로고
    • Order conditions for general two-step Runge-Kutta methods
    • E. Hairer and G. Wanner, Order conditions for general two-step Runge-Kutta methods. SIAM J. Numer. Anal., 34 (1997), 2087-2089.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 2087-2089
    • Hairer, E.1    Wanner, G.2
  • 15
    • 0005340479 scopus 로고
    • Explicit two-step Runge-Kutta methods
    • Z. Jackiewicz, R. Renaut and M. Zennaro, Explicit two-step Runge-Kutta methods. Appl. Math., 40 (1995), 433-456.
    • (1995) Appl. Math. , vol.40 , pp. 433-456
    • Jackiewicz, Z.1    Renaut, R.2    Zennaro, M.3
  • 16
    • 0001472260 scopus 로고    scopus 로고
    • General linear methods with external stages of different orders
    • Z. Jackiewicz and R. Vermiglio, General linear methods with external stages of different orders. BIT, 36 (1996), 688-712.
    • (1996) BIT , vol.36 , pp. 688-712
    • Jackiewicz, Z.1    Vermiglio, R.2
  • 17
    • 0005253227 scopus 로고
    • A representation formula for two-step Runge-Kutta methods
    • ed. E. Lipitakis, September 22-24, 1994, Hellenic Mathematical Society, Athens, Greece
    • Z. Jackiewicz and S. Tracogna, A representation formula for two-step Runge-Kutta methods. Proc. of the Second Hellenic European Conference on Mathematics and Informatics (ed. E. Lipitakis), September 22-24, 1994, Hellenic Mathematical Society, Athens, Greece, 1994, 111-120.
    • (1994) Proc. of the Second Hellenic European Conference on Mathematics and Informatics , pp. 111-120
    • Jackiewicz, Z.1    Tracogna, S.2
  • 18
    • 0001164459 scopus 로고
    • A general class of two-step Runge-Kutta methods for ordinary differential equations
    • Z. Jackiewicz and S. Tracogna, A general class of two-step Runge-Kutta methods for ordinary differential equations. SIAM J. Numer. Anal., 32 (1995), 1390-1427.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1390-1427
    • Jackiewicz, Z.1    Tracogna, S.2
  • 19
    • 21344471075 scopus 로고    scopus 로고
    • Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
    • Z. Jackiewicz and S. Tracogna, Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations. Numerical Algorithms, 12 (1996), 347-368.
    • (1996) Numerical Algorithms , vol.12 , pp. 347-368
    • Jackiewicz, Z.1    Tracogna, S.2
  • 20
    • 84968518141 scopus 로고
    • Variable-stepsize explicit two-step Runge-Kutta methods
    • Z. Jackiewicz and M. Zennaro, Variable-stepsize explicit two-step Runge-Kutta methods. Math. Comp., 59 (1992), 421-438.
    • (1992) Math. Comp. , vol.59 , pp. 421-438
    • Jackiewicz, Z.1    Zennaro, M.2
  • 21
    • 0043242780 scopus 로고
    • Derivation of efficient, continuous, explicit Runge-Kutta methods
    • B. Owren and M. Zennaro, Derivation of efficient, continuous, explicit Runge-Kutta methods. SIAM J. Sci. Stat. Comput., 13 (1992), 1488-1501.
    • (1992) SIAM J. Sci. Stat. Comput. , vol.13 , pp. 1488-1501
    • Owren, B.1    Zennaro, M.2
  • 23
    • 0030400404 scopus 로고    scopus 로고
    • Implementation of two-step Runge-Kutta methods for ordinary differential equations
    • S. Tracogna, Implementation of two-step Runge-Kutta methods for ordinary differential equations. J. Comput. Appl. Math., 76 (1996), 113-136.
    • (1996) J. Comput. Appl. Math. , vol.76 , pp. 113-136
    • Tracogna, S.1
  • 24
    • 0005292548 scopus 로고    scopus 로고
    • Two-step Runge-Kutta methods. Theory and practice
    • S. Tracogna and B. Welfert, Two-step Runge-Kutta methods. Theory and practice. BIT, 40 (2000), 775-799.
    • (2000) BIT , vol.40 , pp. 775-799
    • Tracogna, S.1    Welfert, B.2
  • 25
    • 0342616178 scopus 로고
    • Strategies for deriving new explicit Runge-Kutta pairs
    • J.H. Verner, Strategies for deriving new explicit Runge-Kutta pairs. Ann. Numer. Math., 1 (1994), 225-244.
    • (1994) Ann. Numer. Math. , vol.1 , pp. 225-244
    • Verner, J.H.1
  • 26
    • 0347431773 scopus 로고    scopus 로고
    • High order explicit Runge-Kutta pairs with low stage order
    • J.H. Verner, High order explicit Runge-Kutta pairs with low stage order. Appl. Numer. Math., 20 (1996), 1-13.
    • (1996) Appl. Numer. Math. , vol.20 , pp. 1-13
    • Verner, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.